Methods from Stochastic Analysis, coupled with convex duality techniques, have been very successful in tackling optimization problems that arise in mathematical economics and finance. We survey some "classical" problems of this type, then formulate a model of preferences with non-addictive habits. Here consumption is required to be non-negative at all times but is allowed to fall below a standard-of-living index that aggregates past consumption. We describe the optimal strategies for this problem, and show that the consumption constraint is binding up to a suitable stopping time, after which it becomes slack. Backwards stochastic equations play a crucial role in establishing this result. We describe variants of this problem that remain open; these suggest some very interesting questions in the analysis of forward-backward stochastic equations of a novel type. (Joint work with Jérôme Detemple.)